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A seemingly simple but a challenging quiz, find the nth term in 1,6,30,120.....

I am thinking is a quadratic due to the constant difference but n th term is needed not a recursive one - I got confused

Waitara Mburu
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  • There are infinitely many ways to continue this. Do you have any additional information? – Vasili Nov 15 '18 at 01:39
  • It seems that the formula is multiplying the previous one by $7-n$ with $a_0=1.$ So, $a_1=1(7-1)=6,$ $a_2=a_1(7-2)=30,$ and so on. – William M. Nov 15 '18 at 01:40
  • Sequences are not determined by any finite number of terms. We can only guess. This one looks like $$1,\quad6,\quad6\times5,\quad6\times5\times4,\quad6\times5\times4\times3,\quad\cdots$$ It quickly reaches $0$ and stays there. – mr_e_man Nov 15 '18 at 01:40

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It seems to me like $$ a_1=1$$

$$ a_2=1\times 6 =6$$

$$ a_3 = 6\times 5 =30$$

$$ a_4 =30\times 4 =120$$

$$ a_5 =120\times 3 = 360$$

Thus $$a_1=1, a_2=6$$

And for $n\ge 3$,

$$ a_{n+1} = (8-n)a_n $$

Mohammad Riazi-Kermani
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  • Thank you guys, a friend thought that a polynomial degree 4 could help but obviously that was not correct as that would mean 'continuity!' – Waitara Mburu Nov 15 '18 at 08:52